Pulley & Belt

In the figure shown, a pulley is driven by a belt. What minimum coefficient of friction will prevent slipping between pulley and belt? Ignore centrifugal effects.

Hint
Belt Friction:
$$$F_1=F_2e^{\mu \theta}$$$
where $$F_1$$ is the applied force in the direction of impending motion, $$F_2$$ is the applied force resisting impending motion, $$\mu$$ is the static coefficient of friction, and $$\theta$$ is the total angle of contact between surfaces in radians.
Hint 2
Unit Circle:
Belt Friction:
$$$F_1=F_2e^{\mu \theta}$$$
where $$F_1$$ is the applied force in the direction of impending motion, $$F_2$$ is the applied force resisting impending motion, $$\mu$$ is the static coefficient of friction, and $$\theta$$ is the total angle of contact between surfaces in radians. Recall a unit circle to determine $$\theta$$ :
Therefore,
$$$1,000N=(550N)e^{\mu (1.5\pi-0.5\pi)}$$$
Solving for the coefficient of friction:
$$$ln(\frac{1,000}{550})=ln(e^{\mu \pi})=\mu \piĀ $$$
$$$\mu=\frac{1}{\pi}\cdot ln(\frac{1,000}{550})=\frac{1}{\pi} \cdot 0.5978=0.19$$$
0.19